Finite impulse response filters are widely known in digital signal processing. It is also known that optical delay line circuits comprising cascaded optical delay lines and directional couplers have filter characteristics similar to those of FIR digital filters. It has been shown that coherent, two-port, serially cascaded-form optical delay line circuits can realize arbitrary signal processing functions identical to those of FIR digital filters with complex filter coefficients whilst maintaining a maximum transmission characteristic of 100%.
A paper entitled “Synthesis of Coherent Two-Port Lattice-Form Optical Delay-Line Circuit”, Journal of Lightwave Technology, volume 13, pages 73-82, 1995 authored by Kaname Jinguji (hereinafter referred to as “Jinguji”) and corresponding U.S. Pat. No. 5,572,611 (hereinafter referred to as “the '611 patent”) issued to Nippon Telegraph and Telephone Corporation present a method for synthesizing a coherent two-port lattice-form optical delay line circuit with phase shift controllers as illustrated in FIGS. 1 and 2. The presence of the phase shift controllers enables a tunable optical delay line filter to be implemented.
The optical delay-line circuit illustrated in FIG. 1 is a two-port circuit 10 having two input ports 11, 12 and two output ports 13, 14. The circuit 10 comprises two planar waveguides 15, 16 arranged between the input ports 11, 12 and the output ports 13, 14 in a pair-wise series of N+1 variable, directional couplers 17 and N variable delay lines 18. The variable directional couplers 17 have variable coupling rates and couple together the two planar waveguides 15, 16 of the N variable delay lines 18. The delay lines 18 each have a constant optical path length difference ΔL between their waveguides 15, 16. Each delay line 18 has a phase shift controller 19 on at least one of its waveguides 15, 16 which can be controlled to provide a desired degree of phase difference φ between optical signals being transmitted through the respective waveguides 15, 16. The phase shift controllers 19 may be implemented as resistive heaters applied to a surface of a monolithic silica on silicon waveguide structure, (not shown) comprising the optical delay line circuit 10. The waveguides 15, 16 are formed to be single mode in operation.
FIG. 2 illustrates a variable directional coupler for the optical delay line circuit of FIG. 1. This comprises a symmetric Mach-Zehnder interferometer having two optical waveguides 15, 16 with equal optical path lengths, i.e. ΔL=0, or a small length difference that introduces an optical phase difference between the arms of up to 2π radians. The waveguides 15, 16 are coupled at each end by directional couplers 20 that preferably have a power coupling ratio of 3 dB. Each of the waveguides 15, 16 has a phase shift controller 21 which may be implemented as a resistive heater, although only one of the waveguides 15, 16 may be provided with a phase shift controller 21. The amplitude coupling ratio of the variable directional coupler is given by sin(θ), where θ is the coupling coefficient angle. The phase shift controllers 21 allow the phase difference between the optical waveguides 15, 16 of the variable directional coupler 17 to be changed to the extent that the amplitude coupling ratio sin(θ) of the variable directional coupler 17 can be varied through the range of 1 to 0 to −1.
The filter function of the optical delay line circuit filter is characterized by its wavelength dependent attenuation and chromatic dispersion. Depending on the design and the application of the filter, either the attenuation, the chromatic dispersion or both describe the filter function as used in this document.
The filter function (transfer function) coefficients of an optical delay line circuit filter 10 as illustrated by FIGS. 1 and 2 comprise the strengths of the directional couplers 17 and the phase delays of the delay lines 18. In order to set the filter to a desired filter function (spectral attenuation as a function of optical wavelength), the filter function is decomposed into its FIR coefficients from which the corresponding filter coefficients can be calculated according to Jinguji and the '611 patent. The filter coefficients comprise two sets of parameters, namely the coupling coefficient angles θ of the N+1 directional couplers 17 and the phase shift values φ of the N delay lines 18. Jinguji and the '611 patent teach a method of obtaining these sets of parameters from a set of recurrent equations. Each of the respective sets of parameters, once determined, is implemented through control of its respective set of phase shift controllers (resistive heaters) 19, 21. Thus, from the teaching of Jinguji and the '611 patent, it is in principle possible to provide an N stage serially, cascaded optical delay line circuit filter 10 with a desired filter function.
The solution for a desired filter function calculated in accordance with Jinguji and the '611 patent are for an ideal model of the optical delay line circuit filter 10. In Jinguji and the '611 patent, certain assumptions are made to the effect that all Mach-Zehnder interferometers (delay lines) have the same optical path length difference ΔL, that the amplification/attenuation in both waveguides of a delay line are equal and that the directional couplers are wavelength independent. In a real device, fabrication anomalies etc. will result in an optical delay circuit where all of these assumptions do not hold true. As a result, the filter coefficients calculated in accordance with Jinguji and the '611 patent will not actually define the desired filter function (target filter function) in a real optical delay line circuit filter 10 but define what can be considered as a start filter function. This will be apparent from a resultant, measured response for the optical delay line circuit 10 when the transfer coefficients calculated in accordance with Jinguji and the '611 patent are implemented.
An extended model incorporates fabrication anomalies and other properties of optical delay line circuit such as, among others, the wavelength dependency of the coupling ratio and the propagation loss difference in the waveguide arms of the delay lines and the variable directional couplers 15, 16. The extended model is used to find the optimum values for the coupling coefficient angles θ of the N+1 variable directional couplers 17 and the phase shift values φ of the N delay lines 18 by utilizing a non-linear optimization procedure. The parameters in the extended model that describe the fabrication anomalies and the important optical properties of the N+1 variable directional couplers 17 and N optical delay lines 18 are determined through a separate characterization procedure on the optical delay line circuit 10 that needs to be performed once before the device is set in operation.
An optical delay circuit line filter 10 as illustrated in FIGS. 1 and 2 can be employed, as aforesaid, in a dynamic gain equalizer but it can equally be employed in many other optical signal processing applications such as wavelength dispersion filters, frequency selection filters or polarization mode dispersion equalizers.
The ideal gain curve for an optical amplifier comprises a constant gain over a selected spectrum of optical wavelengths. However, as illustrated in FIG. 3, the gain curve 22 for a real Er doped optical amplifier does not provide constant gain over its spectral width. An equalizer can provide an attenuation curve 23 that seeks to flatten the Er doped amplifier gain characteristic 22 to provide a gain profile 24 tending towards the ideal flat gain profile for an optical amplifier. A problem encountered with optical amplifiers is that their gain profiles vary with time in response to various disparate influences such as operating temperature, input signal power, for example. These variations tend to occur over relatively long time periods in the order of minutes due to temperature variations or degradations, but also over smaller time-scales in the order of 10 ms due to network reconfigurations, rerouting or drop-out of signals at certain wavelengths.
An advantage of a dynamic gain equalizer employing an optical delay line circuit filter 10 as illustrated in FIGS. 1 and 2 is its tunability of the filter function (spectral attenuation) by adapting the filter coefficients in order to vary the spectral attenuation profile of the equalizer in response to changes in the optical amplifier gain profile over time or for any other reason. This can be achieved by linearly changing the filter coefficients from respective start values comprising the current or start filter function to respective target values representative of the desired or target filter function. However, if the filter coefficients (sets of parameters θ & φ) are changed linearly from a start configuration to a target configuration, the attenuation at certain wavelengths during the transition may vary by more than the range spanned by the start and end filter coefficient configurations resulting in undesirable transition phenomena. These might include temporary strong attenuation at certain wavelengths resulting in network failure due to drop-out of said wavelength.
In addition, during the filter function transition, special care must be taken to ensure that the filter coefficients stay within their physically possible ranges. For example, the amplitude coupling ratio sin(θ) of a directional coupler is dependent on the temperature range of that coupler's resistive heaters and many possible θ values for that coupler may not be implementable through its resistive heaters. This problem has been attended to previously by employing the periodicity of the filter function with the filter coefficients by means of adding or subtracting integer periods to those filter coefficients that extend outside their respective physical boundaries. However, such ‘folding’ of the filter coefficients cannot be achieved in a discreet step but must be varied smoothly thus encountering the same problem as aforesaid of the attenuation at certain wavelengths during the transition varying by more than the range spanned by the start and end filter coefficient configurations resulting in undesirable transition phenomena.